A strange thing, my Genesis LED isn't connected

[Ness7281992]

Okay, so the non-TMSS Model 1 Genny I recently acquired (~2 years ago) from a local game shop for $20 seemed to work fine when I tested it, then I started really playing games on it, and i started to notice strange things. Sound would hang or glitch out, a diagonal wouldn't work on Player 1, my generic 6-button didn't work well with some games, but not at all with the entire Streets of Rage series. When I first reaquired Phantasy Star II, it frequently crashed during battles.

Then one day I finally noticed it: the LED doesn't come on. I promptly openned the console, only to find the cord connecting the LED to the system proper was gone and the wires on the LED that poked through their holes on the faceplate were shorter than 5 o'clock shadow. Apparently, someone more the rookie than I tampered with the system and snapped off the LED cord by accident; stranger still, they desoldered any evidence it connected. Now, i know it's supposed to be one of two contacts, but I'm not sure why I have 2 to chose from. I openned my TMSS Model 1 to compare, and it used the one closest to the front, which makes sense, but it also had that extra contact available, cus why not?

Obviously, I can just solder a wire and call it good, but I would rather use something that'll connect to it like a kosher Genny, especially if this doesn't fix the issues I've been having (I'm positive it won't) and I have to keep openning the system. Plus, I don't want to make same mistake years later when a new problem arises. Well, Google search isn't helping me here. I cannot find anything for just a simple Genny LED wire, only LED mods, and they just use the original cord anyway. Yes, I could just buy a For-Parts console and nab it off of that, but paying a (humble)bunch of dough for a wire and components that quite frankly are unreliable seems a little bit of a roundabout way of fixing this. I only need that cord, but I still have the stubby LED to contend with, and I don't really want to alter the case just to swap out the LED. It's a weird situation, but if that connector used to connect the LED to the wire is standardized like the various wires similar in modern PC's, then I could just go that route. Unfortunately, I never learned a name for those connectors, making it kinda hard to Google.

So, do the wire connectors follow a standard? If so, what is it called? Any other advice in fixing this console or prepping it for future repairs?

[RP2A03]

I have no idea what that connector is called, but you can probably find it (or something close enough) in various electronics.